Mayor Michael Bloomberg this afternoon presented a balanced executive budget for the 2013 fiscal year that includes no new taxes, but which includes cuts for social services and relies on at least two funding sources that must still be considered aspirational.

His $68.7 billion budget proposal increases funding for education from $13.3 billion in this fiscal year to $13.6 billion next, which will allow the city to hire more teachers. But that increase is contingent on $300 million in state and federal funding that the city will receive if it comes to an agreement with the teachers union on performance-based teacher evaluations. That agreement has yet to be reached.

"There's no substantive reason why a final agreement should not be reached very quickly," said the mayor. "The longer the U.F.T. waits, however, the longer it will take our schools to get the money they need and that they deserve."

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The budget also relies on a projected $1 billion from the sale of 2,000 new yellow taxi medallions. But those taxi medallions are tied to an Albany agreement on outer-borough taxis, which is now in litigation.

"If we don't get the $1 billion, we 're going to have to cut services in the city dramatically, there's no other alternative," Bloomberg said.

"And if a judge holds you up, then we start laying off people," he added.

Bloomberg said that city-controlled budgetary costs decreased by $110 million this year, but that costs outside of his control, like pension payments, Medicaid, and debt service, increased by $1.9 billion, or 7.2 percent.

The mayor closed this year's budget using $6.2 billion set aside from the boom years, and from 11 rounds of cost-cutting since 2007. A deficit of $3 billion is projected for fiscal year 2014.

Advocates say the budget includes some $170 million in cuts to afterschool programs and child care, as well as the elimination of 20 fire companies.

Both before and after the mayor's budget address, councilmembers protested his proposed cuts to after-school programs and firehouses.

"So, 31 afterschool programs in the Bronx we'll lose," said Brooklyn councilwoman Letitia James, before the mayor's address. "Seventy-two programs in Brooklyn we will lose, 34 programs in Manhattan, 29 programs in Queens, and six in Staten Island."

The mayor, anticipating such criticism, said, during his remarks, "Keep in mind those reductions are against levels of service that our administration raised to historic highs during a better economic time."

In the question-and-answer portion of the budget address, the mayor strongly implied that both the firehouse and social-service cuts would be subject to change.

"Well, number one, we work with the City Council between now and June 30, so we'll see how all of that works out," said Bloomberg, referring to the social-service cuts.

Referring to firehouses, he said, "We'll see how the budget comes out between now and June 30. But let me point out, we have the lowest number of deaths by fire ever in the history of the city since we started keeping numbers …[in] 1916."

In other news, the mayor said New York City had regained 180 percent of the private-sector jobs lost since the depths of the recession, compared to a nationwide rate of 40 percent. The unemployment rate, however, has also risen, something Bloomberg attributed to more people getting back into the job market and looking for employment.

"That said, the slow pace of the national economic recovery and the uncertainties in the global economy have produced challenges in balancing next year's budget and presents challenges in the future that we cannot ignore," he said.

Asked about criticism from councilmembers about his budget cuts, the mayor got testy.

"I don't have a response to it," he said. "I don't have to have a response to everything. People have a right to say what they want and express their views. There's nothing wrong with that. They weren't elected to run the city."

He also had some criticism about how the federal government was handling the eocnomy.

"In the end, we balance our budget," he said. "The federal goverment does not. The federal government prints money. The European countries did that. And eventually it catches up with you, this year, next year, nobody really knows when it's gonna happen."